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Brian drives a certain part of his journey at an average speed of 30 m
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15 Jul 2018, 08:58

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55% (hard)

Question Stats:

50%(01:48) correct 50%(02:26) wrong based on 16 sessions

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Brian drives a certain part of his journey at an average speed of 30 miles per hour and the rest at an average speed of 60 miles per hour. If he drives for 100 miles, is his average speed for the journey greater than 45 miles per hour?

(1) Brian drives for 30 miles per hour for twice the time than he drives for 60 miles per hour.

(2) Had Brian driven at an average speed of 40 miles per hour rather than 30 miles per hour, his average speed for the journey would have been 48 miles per hour.

Re: Brian drives a certain part of his journey at an average speed of 30 m
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15 Jul 2018, 10:25

Brian drives a certain part of his journey at an average speed of 30 miles per hour and the rest at an average speed of 60 miles per hour. If he drives for 100 miles, is his average speed for the journey greater than 45 miles per hour?

(1) Brian drives for 30 miles per hour for twice the time than he drives for 60 miles per hour.This means he travels equal distance at both 30mph and 60mph..So total time taken = 50/30+50/60=150/60=5/2..AVG speed = 100/(5/2)=200/5=40mphSufficient to say NO

(2) Had Brian driven at an average speed of 40 miles per hour rather than 30 miles per hour, his average speed for the journey would have been 48 miles per hour.Let x be at 60mphSo (X/60)+(100-x)/40=(2x+300-3x)/120=(300-x)/120AVG speed =100/(300-x)/120=100*120/(300-x)=48..300-x=100*120/48=250.......X=300-250=50Now we know miles traveled at 60mph is 50 and remaining 50 is at 30mph..Sufficient

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Re: Brian drives a certain part of his journey at an average speed of 30 m
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16 Jul 2018, 07:07

(1) Brian drives for 30 miles per hour for twice the time than he drives for 60 miles per hour.Let Brian drives for t hour at speed of 60, and 2t at speed of 30Total distance = t*60+ 2t*30 = 120ttotal time taken = t+2t = 3tAverage speed = 120t/3t = 40, sufficient to answer.

(2) Had Brian driven at an average speed of 40 miles per hour rather than 30 miles per hour, his average speed for the journey would have been 48 miles per hour.

if 40 and 60 gives Avg speed = 48. that means driving time at 40 speed is more than driving time at 60 ( using alligation principle), Hence we get that in actual driving time at 30 is more than 60 in real question hence the avg speed is less than average of 30 & 60 ie. 45hence it is sufficient to say that average speed is less than 45 miles per hour.